Question 1

Suppose a rental car company uses simple linear regression to develop an equation that predicts the repair costs for each of its vehicles based on the mileage of the car (total miles driven).The company uses the following data on repair costs and miles driven for five of its cars:  The least squares line would predict annual repair costs of $______ for a car with 60,000 miles on the odometer (rounded to the nearest whole dollar).

Accepted Answer

A) 646 
B) 837 
C) 1385 
D) 831,006

Question 2

In simple linear regression, there is an additive relationship between SST, SSR, and SSE: that is, SST = SSR + SSE

Accepted Answer

A) True 
 B)False

Question 3

The coefficient of determination r2, a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y to the total variation in y, and takes on values between 0 and 1.

Accepted Answer

A) True 
 B)False

Question 4

You are attempting to link weekly hours of exercise (x) to blood pressure (y) using simple linear regression and the following data:  The estimated regression equation is y = 90 - 4x.Compute the standard error of estimate.

Accepted Answer

A) 18.21 
B) 14.83 
C) 21.45 
D) 8.42 
E) 26.9

Question 5

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x):  The slope term (b) in the estimated regression equation is -12.The intercept term (a) is 162.Show the 90% prediction interval for sales in a particular case in which price is $6 (that is, for x = 6).Report the upper bound for your interval.

Accepted Answer

A) 102.3 
B) 126.8 
C) 113.4 
D) 144.6 
E) 135.2

Question 6

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 25 data points was used.  Can you use the sample results shown here to reject a β = 0 null hypothesis at the 1% significance level? Explain.

Accepted Answer

A) Yes, since the upper bound on the 95% interval estimate of β is greater than 0, we can reject the β = 0 null hypothesis. 
B) No, since the p-value for the intercept term is greater than the significance level of .01, we can't reject the β = 0 null hypothesis. 
C) No, since the p-value for the coefficient of the x variable is greater than .01, we can't reject the β = 0 null hypothesis. 
D) No, since tstat for the x variable is inside ±2.069, we can't reject the β = 0 null hypothesis.

Question 7

In regression analysis, which of the following is NOT a required assumption about the error term $\varepsilon$?

Accepted Answer

A) expected value of the error term is zero 
B) variance of the error term is the same for all values of x 
C) values of the error term are positive 
D) error term is normally distributed 
E) all of the above

Question 8

In simple linear regression, rejecting the null hypothesis in the key hypothesis test regarding the slope of the "population" line means we haven't yet found sufficient sample evidence that there's a useful linear relationship between x and y.

Accepted Answer

A) True 
 B)False

Question 9

You are attempting to link weekly hours of exercise (x) to blood pressure (y) using simple linear regression and the following data:  In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -4 and a = 90.Produce the 95% confidence interval estimate of expected blood pressure when weekly exercise is 5 hours (that is, for x = 5) and report the upper bound for the interval.

Accepted Answer

A) 85.6 
B) 70.0 
C) 111.8 
D) 93.2 
E) 78.3

Question 10

In simple linear regression, the slope and intercept values for the least squares line fit to a sample of data points serve as point estimates of the slope and intercept terms of the least squares line that would be fit to the population of data points.

Accepted Answer

A) True 
 B)False

Question 11

The following data are available for a simple linear regression analysis attempting to link hours of training (x) to hourly output (y).  The least squares line would predict _______ units of output per hour when training is 7 hours.

Accepted Answer

A) 168 
B) 190 
C) 204 
D) 218 
E) 152

Question 12

The computer output table below shows partial results for a linear regression analysis.To test the "no useful linear relationship" hypothesis, determine tstat for the sample slope-a value that would be entered in the indicated cell of the output table as shown.

Accepted Answer

A) 2.77 
B) 1.43 
C) 3.68 
D) 4.10 
E) 1.74

Question 13

You are attempting to link responses to a job announcement (y) to the number of days the announcement was repeated (x):  The estimated regression equation is y = 7 + 1.0x.Compute the standard error of estimate.

Accepted Answer

A) 4.61 
B) 2.45 
C) 3.67 
D) 5.49 
E) 1.27

Question 14

Which of the following is NOT true regarding the coefficient of determination, r2?

Accepted Answer

A) it is the sum of squares error (SS
E)  divided by the sum of squares total (SST) 
B) it is a measure of the goodness of fit of the estimated regression equation 
C) it takes on values between 0 and 1 
D) it explains the amount of variation in y due to x 
E) none of the above: all are true

Question 15

Partial regression results from a sample of 24 observations are shown below.Determine the value for R2, the coefficient of determination here.

Accepted Answer

A) .547 
B) .796 
C) .866 
D) .686 
E) .717

Question 16

The purpose of regression analysis is to find a mathematical relationship that allows us to:

Accepted Answer

A) predict the value of an independent variable based on the value of a dependent variable. 
B) predict the value of a dependent variable based on the value of an independent variable. 
C) determine whether the average value of one variable, x, differs significantly from the average value of another variable, y. 
D) determine whether two events X and Y are statistically dependent or statistically independent. 
E) determine whether there is a cause-and effect relationship between two variables.

Question 17

A National Football League agent is conducting a simple linear regression study linking completion percentage in a season (x) to salary per game(y) for quarterbacks.The data for five players are shown below.  The slope for the least squares line is 4.4.The intercept is 182.Determine sy.x, the standard error of estimate, that should be entered in the table below.

Accepted Answer

A) 116.34 
B) 67.82 
C) 43.51 
D) 18.19 
E) 21.68

Question 18

In simple linear regression, the least squares line fit to a sample of data points seeks to minimize the maximum distance of points from the line.

Accepted Answer

A) True 
 B)False

Question 19

In simple linear regression, given SSE = 2348 and SST = 3569,

Accepted Answer

A) SSR = 5917. 
B) r2 = .342. 
C) SSD = 1343. 
D) r = .364. 
E) MSE = 892

Question 20

In multiple regression, a single independent variable is linked to a set of two or more dependent variables.

Accepted Answer

A) True 
 B)False

Exam 11: Basic Regression Analysis

In simple linear regression, there is an additive relationship between SST, SSR, and SSE: that is, SST = SSR + SSE

The coefficient of determination r², a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y to the total variation in y, and takes on values between 0 and 1.

You are attempting to link weekly hours of exercise (x) to blood pressure (y) using simple linear regression and the following data: The estimated regression equation is y = 90 - 4x.Compute the standard error of estimate.

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 25 data points was used. Can you use the sample results shown here to reject a β = 0 null hypothesis at the 1% significance level? Explain.

In regression analysis, which of the following is NOT a required assumption about the error term $\varepsilon$ ?

In simple linear regression, rejecting the null hypothesis in the key hypothesis test regarding the slope of the "population" line means we haven't yet found sufficient sample evidence that there's a useful linear relationship between x and y.

In simple linear regression, the slope and intercept values for the least squares line fit to a sample of data points serve as point estimates of the slope and intercept terms of the least squares line that would be fit to the population of data points.

The following data are available for a simple linear regression analysis attempting to link hours of training (x) to hourly output (y) . The least squares line would predict _______ units of output per hour when training is 7 hours.

The computer output table below shows partial results for a linear regression analysis.To test the "no useful linear relationship" hypothesis, determine t_stat for the sample slope-a value that would be entered in the indicated cell of the output table as shown.

You are attempting to link responses to a job announcement (y) to the number of days the announcement was repeated (x) : The estimated regression equation is y = 7 + 1.0x.Compute the standard error of estimate.

Which of the following is NOT true regarding the coefficient of determination, r²?

Partial regression results from a sample of 24 observations are shown below.Determine the value for R², the coefficient of determination here.

The purpose of regression analysis is to find a mathematical relationship that allows us to:

In simple linear regression, the least squares line fit to a sample of data points seeks to minimize the maximum distance of points from the line.

In simple linear regression, given SSE = 2348 and SST = 3569,

In multiple regression, a single independent variable is linked to a set of two or more dependent variables.

Exam 11: Basic Regression Analysis

In simple linear regression, there is an additive relationship between SST, SSR, and SSE: that is, SST = SSR + SSE

The coefficient of determination r2, a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y to the total variation in y, and takes on values between 0 and 1.

You are attempting to link weekly hours of exercise (x) to blood pressure (y) using simple linear regression and the following data: The estimated regression equation is y = 90 - 4x.Compute the standard error of estimate.

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 25 data points was used. Can you use the sample results shown here to reject a β = 0 null hypothesis at the 1% significance level? Explain.

In regression analysis, which of the following is NOT a required assumption about the error term ε\varepsilonε ?

In simple linear regression, rejecting the null hypothesis in the key hypothesis test regarding the slope of the "population" line means we haven't yet found sufficient sample evidence that there's a useful linear relationship between x and y.

In simple linear regression, the slope and intercept values for the least squares line fit to a sample of data points serve as point estimates of the slope and intercept terms of the least squares line that would be fit to the population of data points.

The following data are available for a simple linear regression analysis attempting to link hours of training (x) to hourly output (y) . The least squares line would predict _______ units of output per hour when training is 7 hours.

The computer output table below shows partial results for a linear regression analysis.To test the "no useful linear relationship" hypothesis, determine tstat for the sample slope-a value that would be entered in the indicated cell of the output table as shown.

You are attempting to link responses to a job announcement (y) to the number of days the announcement was repeated (x) : The estimated regression equation is y = 7 + 1.0x.Compute the standard error of estimate.

Which of the following is NOT true regarding the coefficient of determination, r2?

Partial regression results from a sample of 24 observations are shown below.Determine the value for R2, the coefficient of determination here.

The purpose of regression analysis is to find a mathematical relationship that allows us to:

In simple linear regression, the least squares line fit to a sample of data points seeks to minimize the maximum distance of points from the line.

In simple linear regression, given SSE = 2348 and SST = 3569,

In multiple regression, a single independent variable is linked to a set of two or more dependent variables.

The coefficient of determination r², a measure of the goodness of fit of the estimated regression equation, is the ratio of the explained variation in y to the total variation in y, and takes on values between 0 and 1.

In regression analysis, which of the following is NOT a required assumption about the error term $\varepsilon$ ?

The computer output table below shows partial results for a linear regression analysis.To test the "no useful linear relationship" hypothesis, determine t_stat for the sample slope-a value that would be entered in the indicated cell of the output table as shown.

Which of the following is NOT true regarding the coefficient of determination, r²?

Partial regression results from a sample of 24 observations are shown below.Determine the value for R², the coefficient of determination here.